Related papers: $\mathbb{Z}_n$ modified XY and Goldstone models an…
We study a recent generalization proposed for the XY model in two and three dimensions. Using both, the continuum limit and discrete lattice, we obtained the vortex configuration and shown that out-of-plane vortex solutions are deeply…
The two-dimensional XY-model with random phase-shifts on bonds is studied. The analysis is based on a renormalization group for the replicated system. The model is shown to have an ordered phase with quasi long-range order. This ordered…
In this paper, we investigate the XY model in the presence of an additional potential term that independently tunes the vortex fugacity favouring their nucleation. By increasing the strength of this term and thereby the vortex chemical…
The anisotropic frustrated 3D XY model with strong disorder in the coupling constants is studied as a model of a disordered superconductor in an applied magnetic field. Simulations with the exchange Monte Carlo method are performed for…
We study vortex unbinding for the classical two-dimensional XY model in a magnetic field on square and triangular lattices. A renormalization group analysis combined with duality in the model shows that at high temperature and high field,…
We find that a $Z$-string is stable in a wide range of parameter space of the two Higgs doublet model due to a split into a pair of two topological $Z$-strings with fractional $Z$ fluxes. This configuration, a bound state of the two strings…
The phase diagram of the fully frustrated XY model on a honeycomb lattice is shown to incorporate three different ordered phases. In the most unusual of them, a long-range order is related not to the dominance of a particular periodic…
In the present work we discuss non-linear physics problems such as Nielsen-Olesen strings, superconducting bosonic straight strings and static vortex rings. We start with a toy model. We search for antiperiodic solitons of the Goldstone…
As a simplified model of randomly pinned vortex lattices or charge-density waves, we study the random-field XY model on square ($d=2$) and simple cubic ($d=3$) lattices. We verify in Monte Carlo simulations, that the average spacing between…
A picture of confinement in QCD based on a condensate of thick vortices with fluxes in the center of the gauge group (center vortices) is studied. Previous concrete model realizations of this picture utilized a hypercubic space-time…
The unbinding of vortex-antivortex pairs for the classical two-dimensional XY model in a magnetic field is studied. A single such pair is connected by a string of overturned spins, leading to linear confinement. We show that this system…
The anisotropic frustrated three dimensional (3D) XY model with disorder in the coupling constants is simulated as a model of a point disordered superconductor in an applied magnetic field. From a finite size scaling analysis of the…
We study the vortex glass transition in disordered high temperature superconductors using Monte Carlo simulations. We use a random pinning model with strong point-correlated quenched disorder, a net applied magnetic field, longrange vortex…
We show that the third Goldstone mode in the two-species condensate mixtures, which emerges at phase-separation, gets hardened when the confining potentials have separated trap centers. The {\em sandwich} type condensate density profiles,…
The XY-plaquette model is the most straightforward lattice realization of a broad class of fractonic field theories that host quasiparticles with restricted mobility. The plaquette interaction appears naturally as a ring-exchange term in…
We construct a molecule of fractional vortices with fractional topological lump charges as a baby Skyrmion with the unit topological lump charge in the anti-ferromagnetic (or XY) baby Skyrme model, that is, an O(3) sigma model with a four…
We show that the third Goldstone mode, which emerges in binary condensates at phase-separation, persists to higher inter-species interaction for density profiles where one component is surrounded on both sides by the other component. This…
We study the XY model on a spherical surface inspired by recently realized spherically confined atomic gases. Instead of a traditional latitude-longitude lattice, we introduce a much more homogeneous spherical lattice, the Fibonacci…
The Goldstone theorem states that there should be a massless mode for each spontaneously broken symmetry generator. There is no such rotational mode in crystals, however superconducting quantum nematics should carry rotational Goldstone…
A review is given of some well-known and some recent results for two- and three-dimensional (2D and 3D) solitons, with emphasis on states carrying embedded vorticity. Unlike typically stable 1D solitons, 2D and 3D ones are vulnerable to…